Question

Jethro Bodine, the renown scientist, has now undertaken the study of animal intelligence with a vengeance. He has developed a test (the BODINE test) which he believes will test the intelligence of all members of the animal kingdom. For starters though, he decides to test animals which he predicts should have the same intelligence. Below are listed the BODINE test scores for a number of animals in each group.

Possum                   Skunks

     8                            4

     6                            5

     4                            6

     6                            6

     5

a.   Find sx1-x2. (standard error).

b. Find t.

c. Find df (degrees of freedom).

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u₁ = u ₂
Alternative hypothesis: u₁ u ₂

Note that these hypotheses constitute a two-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = sqrt[(s₁²/n₁) + (s₂²/n₂)]
SE = 0.81803
DF = 7
t = [ (x₁ - x₂) - d ] / SE

t = 0.67

where s₁ is the standard deviation of sample 1, s₂ is the standard deviation of sample 2, n₁ is the size of sample 1, n₂ is the size of sample 2, x₁ is the mean of sample 1, x₂ is the mean of sample 2, d is the hypothesized difference between the population means, and SE is the standard error.

Since we have a two-tailed test, the P-value is the probability that a t statistic having 7 degrees of freedom is more extreme than - 0.67; that is, less than -0.67 or greater than 0.67.

Thus, the P-value = 0.524

Interpret results. Since the P-value (0.524) is greater than the significance level (0.05), we have to accept the null hypothesis.